Question

1. Four firms in an industry are considering forming a cartel. They meet in a smok-efilled room to discuss the terms of the cartel and to weigh their options. Each firm has a marginal cost given by MC = 20 + 2q. Demand for the market is given by Q = 400 - 2p.  

a) What is the supply for each firm? For all four firms?

b) Suppose the firms compete. What would be the resulting market prices and quantities under competition? How much would each firm produce and what would their producer surplus be?

Answer 1

In order to compute supply curve, we know p=mc in case of competition,

So p= 20 +2q is supply curve for one firm

In order to compute in aggregate,

q= (p - 20)/2 and Q =4q ie Q = 4(p-20)/2

So, Q = 2p - 40

B) We equate the demand and supply

2p-40 = 400 - 2p ie 4p =440 so p=110 and Q= 180

Every firm will produce = 180/4 =45

In order to compute producer surplus, we have

Variable cost = integrate 20+2q =20q+q^2 =20(45) + 45^2 = 45*65 =2925

Producer surplus which are profits equals

45(110) - 2925 =2025